Three-qubit Groverian measure

2008 ◽  
Vol 8 (10) ◽  
pp. 925-942
Author(s):  
E.-L. Jung ◽  
M.-R. Hwang ◽  
D. Park ◽  
L. Tamaryan ◽  
S. Tamaryan
Keyword(s):  
Geometric Interpretation ◽  
Qubit State ◽  
Phase Factor ◽  
Analytical Expression ◽  
Near Future ◽  
Analytical Expressions ◽  
Qubit States ◽  
Local Unitary Invariance ◽  
Unitary Invariance

The Groverian measures are analytically computed in various types of three-qubit states. The final results are also expressed in terms of local-unitary invariant quantities in each type. This fact reflects the manifest local-unitary invariance of the Groverian measure. It is also shown that the analytical expressions for various types have correct limits to other types. For some types (type 4 and type 5) we failed to compute the analytical expression of the Groverian measure in this paper. However, from the consideration of local-unitary invariants we have shown that the Groverian measure in type 4 should be independent of the phase factor $\varphi$, which appear in the three-qubit state $|\psi \rangle$. This fact with geometric interpretation on the Groverian measure may enable us to derive the analytical expressions for general arbitrary three-qubit states in near future.

scholarly journals On Classes of Local Unitary Transformations

2012 ◽  
Vol 19 (02) ◽  
pp. 283-292
Author(s):  
Naihuan Jing
Keyword(s):  
Homogeneous Spaces ◽  
Unitary Groups ◽  
Mixed States ◽  
Density Matrices ◽  
Double Cosets ◽  
Unitary Transformations ◽  
One To One ◽  
Local Unitary Invariance ◽  
Unitary Invariance

We give a one-to-one correspondence between classes of density matrices under local unitary invariance and the double cosets of unitary groups. We show that the interrelationship among classes of local unitary equivalent multi-partite mixed states is independent from the actual values of the eigenvalues and only depends on the multiplicities of the eigenvalues. The interpretation in terms of homogeneous spaces of unitary groups is also discussed.

Local quantum uncertainty and trace distance discord dynamics for two-qubit X states embedded in non-Markovian environment

2018 ◽  
Vol 32 (20) ◽  
pp. 1850218 ◽  
Author(s):  
Youssef Khedif ◽  
Mohammed Daoud
Keyword(s):  
Quantum Correlations ◽  
Trace Distance ◽  
Markovian Environment ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Limiting Case ◽  
Analytical Expressions ◽  
Qubit States ◽  
Markovian Regime

We investigate the behavior of quantum correlations in some specific Werner-like two-qubit states, where the qubit interacts individually with non-Markovian environment. We employ the local quantum uncertainty and trace distance discord to quantify the amount of quantum correlations between the evolved qubits and the corresponding analytical expressions are derived. For specific values of the parameters characterizing the whole system, the dynamics of quantum correlations exhibits collapse and revival phenomena. The influence of the non-Markovianity is also investigated to analyze the monotonic decay of quantum correlations in the limiting case of Markovian regime. Furthermore, we show that trace distance discord captures quantum correlations that cannot be revealed by local quantum uncertainty in some particular situations.

scholarly journals BEST SEPARABLE APPROXIMATION WITH SEMI-DEFINITE PROGRAMMING METHOD

2004 ◽  
Vol 02 (04) ◽  
pp. 541-558 ◽  
Author(s):  
M. A. JAFARIZADEH ◽  
M. MIRZAEE ◽  
M. REZAEE
Keyword(s):  
Mixed State ◽  
Qubit State ◽  
Programming Method ◽  
Simple Analytical Expression ◽  
Analytical Expression ◽  
Isotropic State ◽  
Separable Approximation ◽  
Isotropic States

The present methods for obtaining the optimal Lewenestein–Sanpera decomposition of a mixed state are difficult to handle analytically. We provide a simple analytical expression for the optimal Lewenstein–Sanpera decomposition by using semi-definite programming. In particular, we obtain the optimal Lewenstein–Sanpera decomposition for some examples such as: the Bell decomposable state, the iso-concurrence state, the generic two-qubit state in the Wootters basis, the 2⊗3 Bell decomposable state, the d⊗d Werner and isotropic states, a one parameter 3⊗3 state, and finally a multi-partite isotropic state.

One-party controlled minimum remote state preparation of equatorial n-qubit states

2014 ◽  
Vol 12 (06) ◽  
pp. 1450038 ◽  
Author(s):  
Yahong Wang ◽  
Hongwei Liang
Keyword(s):  
Quantum Channel ◽  
Ghz State ◽  
Qubit State ◽  
Remote State Preparation ◽  
Bloch Sphere ◽  
State Preparation ◽  
Epr Pairs ◽  
Controlled Remote State Preparation ◽  
Qubit States

This paper offers a theoretical protocol for one-party controlled remote state preparation (RSP) of n-qubit states with minimum resources consumption. We are mainly focused on the case of the n-qubit state chosen from equatorial circle on a Bloch sphere. We use n - 1 EPR pairs and one GHZ state as quantum channel and show that only n + 1 cbits, n ebits and 2n + 1 qubits are consumed during the controlled RSP processing.

Contextuality of a two-qubit state in 4-cycle measurement scenarios

2018 ◽  
Vol 33 (36) ◽  
pp. 1850212
Author(s):  
Hui-Xian Meng ◽  
Wen-Hua Wang ◽  
Jie Zhou ◽  
Jing-Ling Chen
Keyword(s):  
The State ◽  
Qubit State ◽  
Quantum Contextuality ◽  
Qubit States

We introduce a quantity of contextuality, i.e. the maximum contextuality of a two-qubit state in 4-cycle measurement scenarios, to study quantum contextuality of two-qubit states for the 4-cycle noncontextual inequalities. Subsequently, we prove several appealing features of this quantity of contextuality, including the faithfulness, the boundedness, the invariance under unitary operations and the convexity. Remarkably, for arbitrary two-qubit state, we reformulate this quantity of contextuality analytically by eigenvalues of the state. Therefore, in 4-cycle measurement scenarios, we establish an efficient way to distinguish two-qubit states that can reveal contextuality from ones that cannot.

Fast analytical models for texture evolution in anisotropic polycrystals

2020 ◽  
Author(s):  
Neil Ribe ◽  
Olivier Castelnau ◽  
Neil Goulding ◽  
Ralf Hielscher ◽  
Andrew Walker ◽  
...  
Keyword(s):  
Finite Strain ◽  
Seismic Anisotropy ◽  
Texture Evolution ◽  
Analytical Models ◽  
Mantle Flow ◽  
Analytical Expression ◽  
Arbitrary Amplitude ◽  
Individual Grains ◽  
Weighting Coefficients ◽  
Analytical Expressions

<p>To use observations of seismic anisotropy to constrain mantle flow patterns, we need a model for how progressive deformation of a rock leads to preferred orientation (CPO) of its constituent crystals. An important class of such models comprises so-called `self-consistent' (SC) models such as VPSC (viscoplastic SC) and SOSC (second-order SC). However, calculations based on SC models are far too costly for use in 3-D time-dependent convection simulations. To overcome this difficulty, we have developed two new analytical models that combine the accuracy of SC models with a greatly enhanced (by orders of magnitude) computational efficiency. The basis of our new models is the discovery that the crystallographic spin predicted by SC models as a function of crystal orientation is always a generalized spherical harmonic of degree 2, regardless of the CPO of the aggregate. This fact allows us to find an analytical expression for the spin to within an arbitrary amplitude, which we then determine by fitting to the predictions of the SOSC model.  Our first new model, ANPAR, uses the analytical expression for the spin to calculate evolving CPO in an aggregate comprising many (typically 2000) individual grains. The resulting CPO is visually indistinguishable from the SOSC predictions, but is ~ 50000 times faster to compute. Our second model, SBFTEX, is based on a more economical representation of CPO as a weighted sum of a small number of  analytical `structured basis functions' (SBFs), each of which represents the virtual CPO that would be produced by one intracrystalline slip system acting alone. The model consists of analytical expressions for the weighting coefficients of the SBFs as functions of the finite strain experienced by the aggregate. While somewhat less accurate than ANPAR, SBFTEX is ~ 2000 times faster, or ~ 10<sup>8</sup> times faster than SOSC. We will illustrate the predictions of ANPAR and SBFTEX for pure olivine polycrystals, a simple model for the upper 400 km of the mantle.</p>

scholarly journals A scheme for direct detection of qubit–environment entanglement generated during qubit pure dephasing

2020 ◽  
Vol 20 (1) ◽  
Author(s):  
Bartosz Rzepkowski ◽  
Katarzyna Roszak
Keyword(s):  
Thermal Equilibrium ◽  
State Of The Art ◽  
Direct Detection ◽  
Qubit State ◽  
Superposition State ◽  
Initial State ◽  
Pure Dephasing ◽  
Nv Center ◽  
Spin Qubit ◽  
Qubit States

AbstractWe propose a scheme for the detection of qubit–environment entanglement which requires only operations and measurements on the qubit, all within reach of current experimental state-of-the-art. The scheme works for any type of interaction which leads to pure dephasing of the qubit as long as the initial qubit state is pure. The scheme is direct in the sense that it allows the detection of entanglement present in the system at time $$\tau $$ τ after the initialization of the qubit in a superposition state. It requires a measurement on the qubit at time $$\tau $$ τ and a comparison of the post-measurement evolution to the evolution obtained by a modified scheme. It becomes particularly simple when one of the qubit states is neutral with respect to the environment, such as in case of the most common choice of the NV center spin qubit or for excitonic charge qubits, when the environment is initially at thermal equilibrium. In this case, the post-measurement evolution needs to be compared only to the standard decoherence which is obtained without any qubit manipulation after the preparation of the initial state.

scholarly journals THE ANALYSIS OF WATER RELEASE FROM THE HYDRO ACCUMULATION LAKE MODRAC WITH SPILLWAY CURVE AND VOLUME CURVES

2016 ◽  
Vol 1 (14) ◽  
Author(s):  
Nedim Suljić ◽  
Dino Hodžić
Keyword(s):  
Reinforced Concrete ◽  
Water Level ◽  
Maximum Height ◽  
Water Release ◽  
Maximum Capacity ◽  
Analytical Expression ◽  
Hydrological Conditions ◽  
Crest Length ◽  
Analytical Expressions ◽  
Bottom Outlet

Dam Modrac is multiple arched reinforced concrete buttress dam, with nine buttresses and ten arches,which by its technical characteristics and volume of the accumulation is considered as one of the highdams. Crown level of spillway is 200.00 m a.s.l. Crest length is 205.00 m, while the maximum height is27.50 m. To control the water level in the reservoir, under normal hydrological conditions, there arefour basic discharges with maximum capacity around Q = 77 m3/s for the projected state. The papergives an analytical expression of the spillway curve and analytical expressions of amounts of waterdischarge separately for each bottom outlet, which are obtained by conducted measurings. Specialsignificance of this paper gives volume curves for hydro accumulation Lake Modrac for projected stateand the period of use of the system.

Amplitude responses of thin beds: Sinusoidal approximation versus Ricker approximation

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 223-230 ◽  
Author(s):  
Hai‐Man Chung ◽  
Don C. Lawton
Keyword(s):  
Numerical Modeling ◽  
Normal Incidence ◽  
Reflection Coefficients ◽  
Amplitude Dependence ◽  
Dominant Wavelength ◽  
Amplitude Response ◽  
Analytical Expression ◽  
Ricker Wavelet ◽  
Analytical Expressions

The amplitude response of a thin bed with arbitrary upper and lower normal incidence reflection coefficients is studied. Two analytical expressions for the normal incidence amplitude response as a function of the thickness are derived and are both valid for weak reflectivities and for thicknesses below [Formula: see text], where [Formula: see text] is the dominant wavelength. The first expression is based on the substitution of a cosine wave for the source wavelet, and the second is based directly on the analytical expression for a Ricker wavelet. The results calculated from these two expressions are compared to numerical modeling results for a Ricker wavelet for several models. We found that the differences between the two expressions are small, and both are good approximations. Above the [Formula: see text] thickness, the percentage differences increase rapidly for both expressions, implying that the thin‐bed assumptions in both derivations break down rapidly beyond the [Formula: see text] thickness. Below the [Formula: see text] thickness, except in the case where the two reflection coefficients are equal in magnitude but opposite in sign, the amplitude dependence on the thickness is nonlinear.

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